Richard Keogh had given Derby the lead after just five minutes but referee Trevor Kettle halted play midway through the first half and the game was swiftly abandoned.
Meanwhile, Bristol City romped to a 5-0 victory over Plymouth after being four up at half time, while Birmingham saw off Crawley Town 5-1.
Brentford, Cardiff, Carlisle and MK Dons also progressed after being held in 90 minutes.
Bristol Rovers, Millwall, Norwich, Nottingham Forest, Wigan and Wycombe all secured home wins, while Blackburn, Charlton, Ipswich, Rochdale, Barnet and Newport County earned victories on the road to progress to the second round.
League Two newcomers Lincoln lost 2-1 at Rotherham, while Sheffield Wednesday thrashed Chesterfield 4-1.
Fulham left it late to beat Wycombe 2-0 on a drab evening at Adams Park, as Reading beat Gillingham by the same score.
Scunthorpe beat Notts County 6-5 on penalties following a 3-3 draw - County's Matt Tootle missing the decisive kick.
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